jmc

By the Rational Root Theorem, the only possible rational roots are of the form $\pm \frac{a}{b},$ where $a$ divides 2 and $b$ divides 4. Thus, the possible rational roots are $$\pm 1,\pm 2,\pm \frac{1}{2},\pm \frac{1}{4}.$$Checking these values, we find that the rational roots are $\boxed{2,-\frac{1}{4}}.$